All of statistics: a concise course in statistical inference
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|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2010
|
| Edition: | 1., st ed. 2004. Corr. 2nd printing. Softcover version of original hardcover edition 2004 |
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis Klappentext |
| Physical Description: | XIX, 442 Seiten Illustrationen, Diagramme 235 mm x 155 mm |
| ISBN: | 9781441923226 1441923225 |
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MARC
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| 245 | 1 | 0 | |a All of statistics |b a concise course in statistical inference |c Larry Wasserman |
| 250 | |a 1., st ed. 2004. Corr. 2nd printing. Softcover version of original hardcover edition 2004 | ||
| 264 | 1 | |a New York, NY |b Springer |c 2010 | |
| 300 | |a XIX, 442 Seiten |b Illustrationen, Diagramme |c 235 mm x 155 mm | ||
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Contents
I Probability
1
Probability
З
1.1
Introduction
.
З
1.2
Sample Spaces and Events
. 3
1.3
Probability
. 5
1.4
Probability on Finite Sample Spaces
. 7
1.5
Independent Events
. 8
1.6
Conditional Probability
. 10
1.7
Bayes'
Theorem
. 12
1.8
Bibliographic Remarks
. 13
1.9
Appendix
. . . . ,. 13
1.10
Exercises
. 13
2
.Random Variables IC
9,1
introduction
., . , ,. 19
9.
Я
Distribution
Funct.vo.uř!
and Probability
ічтсЇіош
,
.
?,0
2.3
Some
Importam
Discrete Random
Variablen ,., , . .
Я5
2.4
Some Important Continuous Random Variables
.,.,. 27'
2.5
Divariate
Distributions
.,,. 31
2.6
Marginal Distributions
. 33
2.7
independent Random Variables
. 34
2.8
Conditional Distributions
. 36
xiv Contents
2.9 Multivariate
Distributions
and HD
Samples
. 38
2.10
Two Important Multivariate Distributions
. 39
2.11
Transformations of Random Variables
. 41
2.12
Transformations of Several Random Variables
. 42
2.13
Appendix
. 43
2.14
Exercises
. 43
3
Expectation
47
3.1
Expectation of a Random Variable
. 47
3.2
Properties of Expectations
. 50
3.3
Variance and Covariance
. 50
3.4
Expectation and Variance of Important Random Variables
. 52
3.5
Conditional Expectation
. 54
3.6
Moment Generating Functions
. 56
3.7
Appendix
. 58
3.8
Exercises
. 58
4
Inequalities
63
4.1
Probability Inequalities
., . , . . 63
4.2
Inequalities For Expectations
. 66
4.3
Bibliographic Remarks
. 66
4.4
Appendix
. 67
4.5
Exercises
.
()8
5
Convergence of Random Variables
71
5.1
Introduction
. 71
5.2
Types of Convergence
. 72
5.3
The Law of Large Numbers
. 76
5.4
The Central Limit Theorem
. 77
5.5
The Delta Method
. 79
5.6
Bibliographic Remarks
. 80
5.7
Appendix
. 81
5.7.1
Almost Sure and L\ Convergence
. 81
5.7.2
Proof of the Central Limit Theorem
. 81
5.8
Exercises
. 82
II Statistical inference
6
Models. Statistical Inference and Learning
87
6.1
Introduction
. 87
6.2
Parametric and Nonparametric Models
. 87
6.3
Fundamental Concepts in Inference
. 90
6.3.1
Point Estimation
. 90
6.3.2
Confidence Sets
. 92
б.
3.3
Hypothesis Testing
. 94
6.4
Bibliographic Remarks
. 95
6.5
Appendix
. 95
6.6
Exercises
. 95
7
Estimating the CDF and Statistical
Funcţionale
97
7.1
The Empirical Distribution Function
. 97
7.2
Statistical Functional
. 99
7.3
Bibliographic Remarks
.104
7.4
Exercises
. 104
8
The Bootstrap
107
8.1
Simulation
.108
8.2
Bootstrap Variance Estimation
.108
8.3
Bootstrap Confidence Intervals
.110
8.4
Bibliographic Remarks
.115
8.5
Appendix
.,.,.,.115
8.5.1
The Jackknife
.,.115
8.5.2
Justification For The Percentile Interval
. 116
5.6 Exercises
.116
9
Parametric Inference
119
9.1
Parameter of Interest
.120
9.2
The Method of Moments
.120
9.3
Maximum Likelihood
.122
9.4
Properties of Maximum Likelihood Estimators
.124
9.5
Consistency of Maximum Likelihood Estimators
.126
9.6
Equivariance of the mle
.127
9.7
Asymptotic Normality
.128
9.8
Optimality
.130
9.9
The Delta Method
.131
9.10
Multiparameter Models
.133
9.11
The Parametric Bootstrap
. 134
9.12
Checking Assumptions
. . . . ,.135
9.13
Appendix
. 135
9.13.1
Proofs
. 135
9.13.2
Sufficiency
. 137
9.13.3
Exponential Families
. 140
9.13.4
Computing Maximum Likelihood Estimates
.142
9.14
Exercices
. 146
10
Hypothesis Testing and
ρ
-values
149
10.1
The
Wald Test .'.,.152
10.2
p-values
.156
10.3
The
χ2
Distribution
. 159
10.4
Pearson's
χ2
Test
För
Multinomial Data
. 160
10.5
The Permutation Test
. 161
10.6
The Likelihood Ratio Test
. 164
10.7
Multiple Testing
. 165
10.8
Goodness-of-fit Tests
. 168
10.9
Bibliographic Remarks
. 169
lO.lOAppendbc
. 170
10.10.1
The Neyman-Pearson Lemma
. 170
10.10.2The ¿-test
. 170
lO.UExercises
. 170
11
Bayesian Inference
175
11.1
The Bayesian Philosophy
. 175
11.2
The Bayesian Method
. 176
11.3
Functions of Parameters
. 180
11.4
Simulation
. 180
11.5
Large Sample Properties of
Bayes'
Procedures
. . 181
1.1.6
Flat Priors, Improper Priors, and
"Noninformative"
Priors
. . . 181
11.7
Multipararneter Problems
. 183
11.8
Bayesian Testing
. . 184
11.9
Strengths and Weaknesses of Bayesian Inference
. 185
ll.lOBibliographic Remarks
. 189
ll.llAppendix
. 190
11.12Exercises
. 190
12
Statistical Decision Theory
193
12.1
Preliminaries
. 193
12.2
Comparing Risk Functions
. 194
12.3
Bayes
Estimators
. 197
12.4 Mimmax
Rules
. 198
12.5
Maximum Likelihood, Minimax, and
Bayes
. 201
12.6
Admissibility
. . . 202
12.7
Stein's Paradox
.204
12.8
Bibliographic Remarks
. 204
12.9
Exercises
. 204
Statistical Models and Methods
13
Linear and. Logistic Regression
209
13.1
Simple Linear Regression
.209
13.2
Least Squares and Maximum Likelihood
.212
13.3
Properties of the Least Squares Estimators
.214
13.4
Prediction
.215
13.5
Multiple Regression
.216
13.6
Model
Selection
.218
13.7
Logistic Regression
.223
13.8
Bibliographic Remarks
.225
13.9
Appendix
.225
13.10
Exercises
.226
14
Multivariate Models
231
14.1
Random Vectors
.232
14.2
Estimating the Correlation
.233
14.3
Multivariate Normal
.234
14.4
Multinomial
.235
14.5
Bibliographic Remarks
. . . ,.237
14.6
Appendix
.237
14.7
Exercises
.238
15
Inference About Independence
239
15.1
Two Binary Variables
., , . . 239
1.5.2
Two Discrete Variables
., , , ,. 243
15.3
Two Continuous Variables
., . ,.,.,. 244
15.4
One Continuous Variable and One Discrete
.,,.,,.,. 244
15.5
Appendix
.,., . . , .
24Ö
15.6
Exercises
. 248
16
Causal Inference
251
16.1
The Counterfactual Model
.251
16.2
Beyond Binary Treatments
.255
16.3
Observational Studies and Confounding
. , .257
16.4
Simpson's Paradox
.,.259
16.5
Bibliographic Remarks
.261
16.6
Exercises
.,.261
17
Directed Graphs and Conditional Independence
263
17.1
Introduction
.263
17.2
Conditional Independence
.,. 264
17.3
DAGs
. . . 264
1.7.4
Probability and DAGs
.
Я66
17.5
More Independence
Relations
. 267
17.6
Estimation for DAGs
. 9,79,
17.7
Bibliographic Remarks
. '772
17.8
Appendix
. 27?,
17.9
Exercises
.276
18
Undirected Graphs
Й81
18.1
Undirected Graphs
.281
18.2
Probability and Graphs
.282
18.3
Cliques and Potentials
.285
18.4
Fitting Graphs to Data
.286
18.5
Bibliographic Remarks
.286
18.6
Exercises
.286
19
Log-Linear Models
291
19.1
The Log-Linear Model
.291
19.2
Graphical Log-Linear Models
.294
19.3
Hierarchical Log-Linear Models
.296
19.4
Model Generators
.297
19.5
Fitting Log-Linear Models to Data
.298
19.6
Bibliographic Remarks
.300
19.7
Exercises
.301
20
Nonparametric Curve Estimation
303
20.1
The Bias-Variance Tradeoff
.- 304
20.2
Histograms
.305
20.3
Kernel Density Estimation
.312
20.4
Nonparametric Regression
,.319
20.5
Appendix
.324
20.6
Bibliographic Remarks
.325
20.7
Exercises
.325
21
Smoothing Using Orthogonal Functions
327
21.1
Orthogonal Functions and L? Spaces
.327
21.2
Density Estimation
.331
21.3
Regression
. 335
21.4
Wavelets
.340
21.5
Appendix
.345
21.6
Bibliographic Remarks
.346
21.7
Exercises
.346
22
Classification
349
22.1
Introduction
.349
22.2
Error Rates and the
Bayes
Classifier
. 350
22.3
Gaussian and Linear Classifiers
.353
22.4
Linear Regression and Logistic
Regression.356
22.5
Relationship Between Logistic Regression and LDA
.358
22.6
Density Estimation and Naive 'Bayer;
.359
22.7
Trees
.360
22.8
Assessing Error Rates and Choosing a Good Classifier
.362
22.9
Support 'Vector Machines
. 368
22.10
Kernelization
.371
22.11
Other Classifiers
.375
22.12
Bibliographic Remarks
. 377
22.13
Exercises
.377
23
Probability
Redux: Stochastic Processes
381
23.1
Introduction
.381
23.2
Markov Chains
.383
23.3
Poisson
Processes
.394
23.4
Bibliographic Remarks
.397
23.5
Exercises
.398
24
Simulation Methods
403
24.1
Bayesian Inference Revisited
. 403
24.2
Basic Monte Carlo Integration
. 404
24.3
Importance Sampling
. 408
24.4
MCMC Part I: The Metropolis-Hastings Algorithm
. 411
24.5
MCMC Part II; Different Flavors
. 415
24.6
Bibliographic Remarks
., . . 420
24.7
Exercises
. 420
index
43
л
This book is for people who want to learn probability and statistics quickly. It brings
together many of the main ideas in modern statistics in one place. The book is suit¬
able for students and researchers in statistics, computer science, data mining, and
machine learning.
This book covers a much wider range of topics than a typical introductory text on
mathematical statistics. It includes modern topics like nonparametric curve estima¬
tion, bootstrapping, and classification, topics that are usually relegated to follow-
up courses. The reader is assumed to know calculus and a little linear algebra. No
previous knowledge of probability and statistics is required. The text can be used
at the advanced undergraduate and graduate levels.
Larry
Wasserman
is Professor of Statistics at Carnegie Mellon University. He is also
a member of the Center for Automated Learning and Discovery in the School of
Computer Science. His research areas include nonparametric inference, asymp¬
totic theory, causality, and applications to astrophysics, bioinformatics, and genet¬
ics. He is the
1999
winner of the Committee of Presidents of Statistical Societies
Presidents' Award and the
2002
winner of the Centre
de recherches mathéma¬
tiques de
Montreal-Statistical
Society
of
Canada
Prize in statistics. He is Associate
Editor of The Journal of the American Statistical Association and The Annals of
Statistics. He is a fellow of the American Statistical Association and of the Institute
of Mathematical Statistics. |
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| bvnumber | BV042210217 |
| classification_rvk | QH 231 SK 800 SK 830 SK 840 |
| ctrlnum | (OCoLC)898023392 (DE-599)DNB1008418013 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1., st ed. 2004. Corr. 2nd printing. Softcover version of original hardcover edition 2004 |
| format | Book |
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| id | DE-604.BV042210217 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T01:58:51Z |
| institution | BVB |
| isbn | 9781441923226 1441923225 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027648935 |
| oclc_num | 898023392 |
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| owner_facet | DE-11 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-824 DE-945 |
| physical | XIX, 442 Seiten Illustrationen, Diagramme 235 mm x 155 mm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in statistics |
| spelling | Wasserman, Larry 1959- Verfasser (DE-588)128738952 aut All of statistics a concise course in statistical inference Larry Wasserman 1., st ed. 2004. Corr. 2nd printing. Softcover version of original hardcover edition 2004 New York, NY Springer 2010 XIX, 442 Seiten Illustrationen, Diagramme 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3598299&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027648935&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027648935&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Wasserman, Larry 1959- All of statistics a concise course in statistical inference Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 |
| title | All of statistics a concise course in statistical inference |
| title_auth | All of statistics a concise course in statistical inference |
| title_exact_search | All of statistics a concise course in statistical inference |
| title_full | All of statistics a concise course in statistical inference Larry Wasserman |
| title_fullStr | All of statistics a concise course in statistical inference Larry Wasserman |
| title_full_unstemmed | All of statistics a concise course in statistical inference Larry Wasserman |
| title_short | All of statistics |
| title_sort | all of statistics a concise course in statistical inference |
| title_sub | a concise course in statistical inference |
| topic | Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3598299&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027648935&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027648935&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wassermanlarry allofstatisticsaconcisecourseinstatisticalinference |